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Rachel98

  • 2 years ago

I don't really get this. Question: Use the rules for exponents and roots to prove that 512^2/3 = 16^3/2

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  1. mjr632
    • 2 years ago
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    Do you mean a rigorous formal proof?

  2. Rachel98
    • 2 years ago
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    I don't really know. This is what the question was and I don't get it.

  3. mjr632
    • 2 years ago
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    Do you understand how to use logarithms?

  4. Rachel98
    • 2 years ago
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    No

  5. mjr632
    • 2 years ago
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    Ah, you will want to understand natural logarithms for this question, I can explain it.

  6. mjr632
    • 2 years ago
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    \[y = \log_b x\] \[x = b^y\]

  7. mjr632
    • 2 years ago
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    If we take the natural logarithm of \[512^{\frac{2}{3}}\] \[\frac{2}{3}\ln(512)\]

  8. mjr632
    • 2 years ago
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    We can pull the exponent out

  9. Rachel98
    • 2 years ago
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    So, is that a cube root? That we ended up with?

  10. precal
    • 2 years ago
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    |dw:1360950294527:dw|

  11. precal
    • 2 years ago
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    |dw:1360950347726:dw|

  12. precal
    • 2 years ago
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    |dw:1360950360574:dw|

  13. precal
    • 2 years ago
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    |dw:1360950390774:dw|

  14. precal
    • 2 years ago
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    |dw:1360950432326:dw|

  15. precal
    • 2 years ago
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    yes they are both equivalent

  16. Rachel98
    • 2 years ago
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    Thanks, so much. That makes sense now.

  17. precal
    • 2 years ago
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    yw

  18. precal
    • 2 years ago
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    no need to use logs here

  19. ghass1978
    • 2 years ago
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    just using exponents :512=2^9 so 512^(2/3)=2^6 and 16^(3/2)=2^6 so both are equal

  20. Rachel98
    • 2 years ago
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    Thanks

  21. precal
    • 2 years ago
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    yw

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